Complex networks have become the dominant paradigm for dynamic modeling of interacting systems. However, networks are inherently limited to describe the interactions of node pairs, while real-world complex systems are often characterized by high-order structures. Furthermore, interaction behaviors based on structure take place among more than two nodes at once [1]}. Empirical studies reveal that high-order interactions are ubiquitous in many complex systems, and such community behaviors play key roles in physiological, biological, and neurological field. In addition, high-order interactions can greatly affect the dynamics of networked systems, ranging from diffusion[2]}, synchronization[3]}, to social evolution processes[4]}, and may lead to the emergence of explosive transitions between node states. For a deeper understanding of the network pattern structure, we can model it via set systems from the perspective of algebraic topology. For example, high-order structures, such as hypergraphs and simplicial complex are better tools for characterizing many social, biological systems[5]}. In addition to recognize the high-order structure in the network, it is important to measure the interaction information of the different structures. Applying simplex structure to complex networks due to its powerful mathematical representation and fully quantifying structure interaction information is the key to the performance of link prediction.
